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Gomory has transformed the integer programming problem into a related group optimization problem which can be more easily solved. An optimal solution to the group problem is optimal for the integer programming problem from which it is derived if the solution is feasible. An algorithm (IP Algorithm I) for solving the group optimization problem is developed, and sufficient conditions on its use are given. The usefulness of IP Algorithm I is extended by amending it to find alternative optima. In a subsequent paper, this algorithm is extended to an algorithm that can solve any integer programming problem.
Jeremy F. Shapiro (Thu,) studied this question.